Cole Lane
06/04/2024 · Elementary School
Solve the compound inequality.
\( 5
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the compound inequality \( 5 < x - 19 < 11 \), we can break it down into two separate inequalities:
1. \( 5 < x - 19 \)
2. \( x - 19 < 11 \)
Let's solve each inequality step by step.
### Solving the first inequality:
1. \( 5 < x - 19 \)
2. Add 19 to both sides:
\[
5 + 19 < x
\]
\[
24 < x
\]
This can be rewritten as:
\[
x > 24
\]
### Solving the second inequality:
1. \( x - 19 < 11 \)
2. Add 19 to both sides:
\[
x < 11 + 19
\]
\[
x < 30
\]
### Combining the results:
Now we combine the two results:
\[
24 < x < 30
\]
### Writing in interval notation:
The solution in interval notation is:
\[
(24, 30)
\]
Thus, the solution set is \( (24, 30) \).
Quick Answer
The solution set is \( (24, 30) \).
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